A stochastic programming approach to the estimation of shell fragmentation distributions

Upon detonation, a shell shatters into large number of fragments. The characteristics of the fragmentation can be expressed using a joint distribution of three properties of the fragments, i.e. velocity, mass and the polar angle of projection. The conventional method of estimating this distribution was to build a thick plywood wall in a half-circle. This ‘arena’ was taken down and dissected after each series of experiments. In addition to being expensive, the technique gave rather imprecise results. This article presents a new experimental method of estimation using test equipment consisting of metal containers called ‘collectors’ and Doppler type radars which are not destroyed by the analysis. The data obtained from this equipment allows the authors to write the estimation problem in the form of a stochastic program with simple recourse into which the entropy related to this random experiment is introduced. With a validation technique based on simulation, they are able to show that this new method of estimating fragment distributions is both reliable and effective.